i disagree with your assumption that an automata could somehow behave exactly like you

like, that doesn't make any sense, you can't know what your actions are without you performing them, we can't magically step outside of space and time and look at our reality like the pages of a comic book, your actions are per definition unique to your specific configuration of particles. It's like how two books can be identical but obviously they're not literally the same book, because they're in different places in space.

your line of reasoning feels a lot like all of the paradoxes, it's a neat thing to think about but ultimately there's the extremely trivial solution of "well that's not possible so it's a nonissue"